Translate a vector of Gumbel parameters into a vector of parameters for a renewal model

Translate a (named) vector of Gumbel parameters into a vector of parameters for a renewal model.

Usage

gumbel2Ren(parGumbel,
           threshold = NULL,
           lambda = NULL,
           w = 1,
           distname.y = c("exponential"),
           vcovGumbel = NULL,
           jacobian = TRUE,
           plot = FALSE)

Arguments

parGumbel

Named vector of Gumbel parameters, with name "scale" and "shape".

threshold

The threshold for the target Renouv parameters.

lambda

The rate for the target Renouv parameters.

w

A block duration for the conversion.

distname.y

The distribution of the excesses.

vcovGumbel

A covariance matrix for the Gumbel parameters.

jacobian

Logical. If TRUE, the jacobian is used.

plot

Logical. If TRUE, a rough plot will be drawn.

Details

Given a vector of Gumbel parameters and a block duration, there exits an infinity of Renouv models with exponential excesses leading to the prescribed Gumbel distributions for the maximum of the marks on a block with duration w. One of these models may be chosen by specifying either a threshold or a rate lambda.

Value

A vector of Renouv parameters, which can be used with

RenouvNoEst.

Author

Yves Deville

Caution

All Renouv models lead to the same return level curve whatever be the choice of threshold or lambda. However, when a covariance matrix is given, the covariance matrix for the Renouv parameters and consequently the confidence bounds depend on the threshold or rate. So the computed covariance matrix must in general be considered as putative.